Theorem or42 221

Description: Rearrangement of 4 disjuncts.

Assertion

Ref	Expression
or42	⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))

Proof of Theorem or42

Step	Hyp	Ref	Expression
1		or4 220	. 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ)))
2		orcom 209	. . 3 ⊢ ((ψ ∨ θ) ↔ (θ ∨ ψ))
3	2	orbi2i 214	. 2 ⊢ (((φ ∨ χ) ∨ (ψ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))
4	1, 3	bitr 151	1 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))

Syntax hints:   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  biass 511

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197

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